Mathematika

Table of Contents - June 1999 - Volume 46, Issue 01  

Research Article

Estimates of the least prime factor of a binomial coefficient

S. V. Konyagina1

a1 Dept. of Mech. and Math., Moscow State University, Moscow, 119899, Russia. e-mail: kon@nw.math.msu.su

Abstract

Let k be a positive integer and g(k) be the least integer n > k + 1 such that all prime factors of are >k. We prove that

S0025579300007555_eqnU1

where c is an absolute positive constant. We also establish a new theorem on the distribution of fractional parts of a smooth function.

(Received May 20 1997)

Key Words:

  • 11B65: NUMBER THEORY; Sequences and sets; Binomial coefficients

Footnotes

Dedicated to the memory of Paul Erdős